A few weeks ago we were invited to talk at the Computer Based Maths Summit on the panel concerned with STEM (Science, Technology, Engineering and Maths) Skills for University and Industry.

It was a fabulous event, with lots of interesting people coming together to share their successes to date and plans for the future and included some impressive presentations using Mathematica from school students that love maths.

The full video of our talk will be going online in February next year, but in the meantime you watch this video of our presentation.STEM skills for Industry

If you’d like to explore some of these maths ideas with us in your classroom, please don’t hesitate to get in touch!

Isn’t that thrilling, that we live in a country in which establishments, such as the RS, inform government policy? Additionally, in order to ensure that the committee thinks outside of their comfort zone, they have been inviting a wide range of people to present to them. How great is that?

The Amazing School was there on the same day as Conrad Wolfram (of WolframAlpha), and we were both talking about the benefits of making maths a more applied subject.

You can watch a version of the talk we gave to the Royal Society here. It’s about 12 minutes long – enjoy!

We rather like the fact that Conrad presents a compelling argument for computer based maths education, from a motivational and utility point of view, and that we show that teaching in this way is also psychologically easier. The key point to remember is that we don’t have to choose between a vocational or academic approach, teaching in a vocational way, using practical examples results in students developing better life skills AND developing a better abstract (academic) skills.

Now, all we need is some schools and maths departments that want to explore this space with us. We teach mathematical reasoning and basic programming skills by using Excel (www.indexmatch.co.uk). We think this is a great way to inspire kids as the software is readily available, and it prepares them with skills that employers seek. If you are a school, or maths teach, and would like to see what we have to offer then GET IN TOUCH!

Our maths education company (www.indexmatch.co.uk) is going from strength to strength, and we have more content coming soon, but I’ve been aware that our courses are for adults and not (currently) for children, and I’ve been wanting to find companies that have developed mathematical training for kids based on established scientific principles.

There are some great arithmetic products out there! Mostly, they focus on adaptive training and motivational factors, by which I mean they make the sums get harder in response to the ability of the child and create fun, playful environments. This is FANTASTIC, it has been reliably shown in numerous experiments that optimal learning happens when the task difficult is as hard as you can manage without failing. A useful analogy is to think about muscles, muscles get stronger fastest if you train at the limit of your ability!

One such company is www.mathsgarden.com, which, in collaboration with the University of Amsterdam, has created a online course for kids based on exactly this kind of adaptive training. A great benefit of this approach when used within schools is that the teacher has excellent data on the performance of each child, without having to do the marking and so has more time to engage one-on-one with children that need help.

IndexMatch seems to be one of very few companies that provide training in mathematics rather than arithmetic. Another notable company is Wolfram (http://www.wolfram.com/training/courses/education/) who have created Wolfram Alpha and Mathematica in order that people can engage in mathematics and not arithmetic.

We’ve moved the original Amazing School blog to a new home, and brought across some of the old content to keep some sense of a narrative thread. Together with the new Cauldron site and the launch of some of our first products, it’s an exciting time for the Amazing School!

“It is evident to those who understand the child of the elementary school that the only processes of acquisition, the only processes of assimilation that are in harmony with his abilities to think, are those that he experiences in close contact with the real, the actual.

Let the child prepare for life by living.

Organise the environment to afford adequate stimuli for the tendencies favourable to development.” - Ovide Decroly

Isn’t that gorgeous? ”Let the child prepare for life by living.” Provide the child with real physical experience that allow him to explore his environment and his natural curiosity will teach him all he has to know.

“To educate in its fullest sense is to create conditions in which the child can live – and is led by these conditions led to live-as fully as possible through each succeeding stage of his development, meeting and solving in his own experience the problems of each stage as it comes, and so gaining the power to meet and to solve the problems that await him in further stages. Such conditions it is for a school to provide.” (Decroly cited by Badley, Dr. Ovide Decroly ed. Albert Decordier, Amicale Rijksbasisonderwijs, Ronse, Belgium)

The job therefore of a school and teachers is to provide the natural environment and activities that will encourage exploration and contribute to concrete learning.

“The essential defect of the elementary school curriculum to my thinking lies in this, it has been the work of men learned in their specialties, but too little concerned with child psychology. And in every attempt that has been made with a view to bettering it the result has been the addition of new subject matter conceived in the same spirit. Thus, nothing has been gained, rather the curriculum has become correspondingly overloaded and more indigestible.” – Ovide Decroly

How true that is! There has been a proliferation of subjects; maths, reading, writing, biology, physics, chemistry, geography, history, English language, English literature, economics …. I’m exhausted already.

Since leaving school there has only been one subject; a problem that needed a solution to be solved using any skills, resources or knowledge at my disposal and even better collaborating with others who had different skills, resources or knowledge.

“Ever since we have taken the trouble to study the child himself in order to uncover the true basis of a natural pedagogy, we have known that only bio-psychological interest can provoke and hold his attention, can direct and control his mental assimilation. We have known, too, that the native interests of children in all countries lie outside of the school as it has been conceived by the exponents of a logical pedagogy. We have known that the continuous action of a well-chosen environment can of itself kindle the activities appropriate to development and permit the child a true and entire realisation of his personality.

It is necessary then that the study of nature conceived in the active sense as a matter or practical experience and effect utilisation of the surroundings, should be the centre of a program of subject matter based on pedagogy. As a result the well-considered teaching of natural sciences must be accorded a more important place in our programs, a place beside the mother tongue as the core of the curriculum.”

By the teaching of Natural Sciences I understand Decroly to mean that children’s learning should be routed in physical interaction, exploration and manipulation of their environment. And as we say in the last article it has now been shown scientifically that he was right, gardening is good for our children.

“Schools which integrate gardens into the curriculum are developing children who are much more responsive to the challenges of adult life.”

Dr Simon Thornton Wood – Royal Horticultural Society

The simple truth is that the child is fascinated by nature and his relationship to nature and how nature supplies his needs and how he can nurture nature. By bringing these into school children feel safe in the world because nature is their friend who can supply their needs for food, shelter, warmth growth and community. And they learn good practical skills, patience, observation, natural science … etc … AMAZING!

There is mounting evidence in favour of delaying formal teaching of abstract skills (reading, writing and arithmetic) until pupils are developmentally ready.

In order to learn to write, a number of prerequisites are necessary. Among others the following are required; concentration, visual acuity, motor dexterity and grasp of language.

What does the evidence tell us about the development of these prerequisites?

Children’s visual acuity reaches adult levels between 4 and 7. Motor dexterity, in particular fine motor control needed to manipulate a pencil, is not usually fully developed until at least 5 years and studies suggest it is slower to develop in boys. In the first years of life children are rapidly learning spoken language. As any person who has spent time with young children knows the rate of language acquisition is very different between children. Studies show that between the ages of 2 years at the earliest and 4 years at the latest children start to grasp complex grammar (negations and questions) but they don’t often perfect it until later and are often still gasping language subtleties until the age of 10.

In summary this shows that development is very different between children. One child may be ready to learn to read at 4 but another might not be ready until 7. It may very well be the case that most (over half) of children are ready for formal tuition aged 5 but it is arguably also the case that nearly all (90%+) are ready by aged 7.

What is the impact of this 2 year delay?

This is practically impossible to test experimentally. However, our European neighbours tend not to progress formal teaching of abstract skills until the age of 7 and often overtake English students in reading writing and maths test by the age of 8. This suggests that being developmentally ready allows the children to progress much faster. It also makes sure that far fewer children develop aversions to reading, writing or arithmetic from having been forced to engage in a task that is physically or cognitively beyond them.

Delaying formal teaching until the age of 7 does not mean children cannot continue to go to school, nor does it mean that children should not be developed. Lots of activities can be done with 5-7 year olds to prepare them for reading, writing and arithmetic in away that is physically and psychologically gentle on the child.

The key change the Amazing School project want to bring into education is an evidence based approach. Let me explain.

In medicine, construction, law enforcement and consumer technology to name just a few, the advances that we have seen over the last 100 years have largely been the result of the scientific method. When a doctor offers you new drugs for an illness you rightly expect and assume that the drug has been through a clinical trail and that the results have been peer reviewed and that the results are significantly more effective than a placebo. When a construction company want to build the newest, highest skyscraper in an earthquake zone they turn to teams of engineers that understand how to model the stresses and strains of these buildings and how the construction materials will interact. This results in safe buildings that won’t collapse. In order to improve law enforcement, crime scene investigators comb through the evidence to reconstruct what happened. When I was growing up no one had a mobile phone, now I have an iPhone in my pocket. All these advances have been due to incremental increases to our knowledge that we have gained via the scientific method.

As far as I can see this does not happen in education. Academics are improving their understanding of memory, attention, perception, cognition, emotion, motivation and many more areas, but these are not reaching mainstream education.

Concurrently, education, which is hungry for modern approaches, latches onto pseudo-science. Ben Goldacre writes a scathing chapter on the pseudo-scientific nonsense that is Brain Gym. Here is a link to one of his articles if you haven’t come across this before:

I’m not trying to argue that science is perfect or that it gets everything right all the time. I just love the scientific approach; make hypotheses that are falsifiable, run a controlled experiment, examine the results using statistics, interpret the results, repeat. With thousands of scientists using this method all over the world, examining different questions the evidence mounts up behind the correct theories and assumptions and we end up with useful models of reality.

I’d love to see this knowledge come into schools and for schools to play a part in testing the application of scientific conclusions.

Here is an example of how what is known scientifically can be applied in education. Memory is a very well studied area of the brain. We know that retrieval is related to the context and the salience of cues. This is why loci techniques (such as memory palaces) work so well; they create clear cues within a context that can be accessed from anywhere. I finally taught myself these memory palace techniques last year. They are so easy to learn. I could memorise 100 studies in about an hour and I still know them now!

When I tell people about the Amazing School project, people love the sound of it but the bravest do point out that it might be a little idealistic / unrealistic.

This is a valid challenge. It’s also a saddening challenge, as it highlights how impotent we feel as adults. It shows that we don’t feel we have the power to create an education system that will delight, amaze, nurture, challenge, motivate and educate our children.

I might have given up. I might have never decided that I would put time and effort (lots of time and effort) into developing this project. But, thankfully for me and my community and you and your children, I didn’t give up. The reason I didn’t give up is because I went to an Amazing School.

The Original Amazing School is in Brussels. It’s not called the Original Amazing School, that would be silly. It’s called Ecole Hamaide and their website is here:

Yup, I went to a school in a fairy tale castle. I learnt more there than I have learnt anywhere else and I left believing that by concentrating, observing, communicating and collaborating we can achieve anything we put our mind to with time. BIG PROBLEMS like nuclear fusion and a cure for AIDS might take a long time mind, but I’m an optimist, I think it is possible.

Perhaps more importantly, I enjoyed my primary school experience and developed a life long love of learning.

I have a deep and abiding love of maths. Largely I think this is due to how I was taught.

I was lucky to have three amazing maths teachers; my mum, Peter Watts and then Dennis Archer.

The fundamental approach all these teacher took was that they understood that maths was simply an abstract language (just like writing) and that it was useful because you can use it to solve interesting real world problems.

I could talk about the maths exercises that excited me the most for hours. Really! They were that memorable and enjoyable. But it may not be particularly interesting to read about! So instead here is a 16 TED lecture on exactly the type of maths education I had.

This video entertainingly demonstrates that formulating the problem one-self helps with understanding the answer and the implication is that this results in lifelong rather than short term learning.

To a large extent this is counterintuitive. Why should maths problems be harder to understand when all the parts are broken down and all the right information is given? There must be a reason, yet psychological research does not yet have an answer to this fascinating question, which probably lies at the heart of intelligence.

I have my suspicions about why formulating the questions aids comprehension. My speculation is that it relates to how the frontal lobe responds when it creates a simulation of the situation and what related knowledge and tools come to bear when this happens. In this view I’m aligning myself with Piaget in his belief that concrete experience is crucial in order to understand the world and with the very recent work of Lakoff and Johnson (1999) who conclude that conceptual knowledge is grounded in experience and concrete sensori-motor information and that abstract knowledge is grounded in metaphor.